We prove that the transition function is a positive contraction Co semigroup on a subspace C1 of l∞. We obtain that the generator of the Markov integrated semigroup is densely defined in l∞ if and only if q-matrix Q is uniformly bounded. At the same time, a sufficient and necessary condition for a transition function to a Feller-Reuter-Riley transition function, is also given. Finally, in an ordered Banach space, a generation theorem is obtained for the increasing integrated semigroup of contractions.%证明了转移函数是l∞的一个子空C1上的正的压缩C0半群,其极小生成元恰好是Markov积分算子半群的生成元在C1中的部分;Markov积分算子半群的生成元稠定的充分必要条件是q-矩阵Q一致有界;同时转移函数是Feller-Reuter-Riley的充要条件是Markov积分算子半群的生成元在c0中的部分产生一个强连续半群.最后,在序Banach空间给出了增加的压缩积分算子半群的生成定理.
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